Answer:
[tex]\[\frac{y^{12}}{8 \times x^{18}}\][/tex]
Step-by-step explanation:
Given expression is [tex]\[(2x^{6}/y^{4})^{-3}\][/tex]
In order to simplify the expression, we need to evaluate the numerator and denominator values when a power of -3 is applied to them individually.
Computing the numerator:
[tex]\[(2x^{6})^{-3}\][/tex]
[tex]\[=(2^{-3} \times x^{6*(-3)})\][/tex]
[tex]\[=(\frac{1}{2^{3}} \times x^{-18})\][/tex]
Similarly the denominator:
[tex]\[(y^{4})^{-3}\][/tex]
[tex]\[=y^{4*(-3)}\][/tex]
[tex]\[=y^{-12}\][/tex]
So the overall simplified expression is:
[tex]\[\frac{(\frac{1}{2^{3}} \times x^{-18})}{y^{-12}}\][/tex]
[tex]\[=\frac{y^{12}}{8 \times x^{18}}\][/tex]
